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So What do we need to know• Flow types• Flow processes• How these control sediment movement or control/influence

sedimentation• How these are represented in the rock record

To begin: What forces control the behavior of fluids:• Inertial forces• Gravitational forces• Viscous forces

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Fluid (def): Cannot withstand any tendency by a deviatoric stress to deform it (i.e., has no strength)

Gas – loose configuration of molecules - AIR

Liquid – tighter configuration of molecules. Can form a free surface. - WATER

Properties of Fluid relevant to the study of sediment transportρ = density, mass per unit fluid volume water vs. air – larger particles by waterμ = dynamic viscosity (a measure of the internal friction of a fluid) has units of stress/strain rate → Pa/(1/t) = Ns/m2 = Pas

suppress turbulence – erosion and entrainment

Sediment Transport and Fluid Flow

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sm

mkgmskg 2

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Air μ ~ 10-5 PasWater (20°C) μ = 10-3 PasIce μ ~ 1010 Pas

Air ρ ~ 1 kg/m3

Water ρ ~ 103 kg/m3

Ice ρ ~ 103 kg/m3

Properties of Flow relevant to the study of sediment transport

U L= scale velocity = scale length

Kinematic viscosity

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Reynolds Number

• Difference in laminar and turbulent flow arise from the ratio of INERTIAL FORCES to VISCOUS FORCES

• INERTIAL FORCES are related to the scale of velocity of fluids in motion and cause turbulence

• VISCOUS FORCES increase with increasing VISCOSITY of the fluid and resist deformation of a fluid and suppresses turbulence

Inertial Force

Viscous Forces

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Reynolds Number

Re <1 Laminar flow: stable to small disturbancesRe >> 1 Turbulent flow: unstable to small disturbances, stretching and twisting

In nature you always have disturbances, question is when do they decay versus grow?

Re < 500 laminarRe > 500 turbulent (Dominant style for natural flows of water and air.)

Laminar flow (in pipe)Stable condition: Perturbations to the flow decay with time.

Turbulent flow (in pipe)Perturbations grow with time.

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Froude Number

• The ratio between INERTIAL and GRAVITY FORCES is the Froude Number.

• In addition to the effects of fluid VISCOSITY and INERTIAL FORCES, GRAVITY also plays a role in fluid flow because GRAVITY influence the way in the fluid transmit surface waves.

• Boundary between a number less than 1 and more than 1 marks change in flow TRANQUIL to RAPID

Inertial Force

Gravitational Forces

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Froude number:

applicable to all flows having a free surface.

Fr < 1 waves can propagate both upstream and downstream, Tranquil (calm) flow.Fr > 1 wave cannot propagate upstream, Shooting flowFr = 1 hydraulic jump, all upstream propagating waves are ‘stuck’ here

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Important definition:= Boundary shear stress

Cd = hydraulic drag coefficient(this coefficient is a complicated function of system properties)

Boundary shear stress can be related to the mean flow velocity, <u>.

= Shear velocity

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Basic Simplifying Assumption: Boundary shear stress, b, characterizes near bed conditions for sediment transport.

Key connections between solid and fluid phase 1. 2.

Flow Properties:

Is associated with Initial Motion:Definition: Movement of a significant number of particles

Terminal velocity of falling particle

Sediment Properties:

13Wiberg and Smith (1985)

Critical Shear Stress, cr :Near-bed conditions associated with the initial motion of a particular grain size are characterized by cr.

Critical shear stress is often presented in the dimensionless form* = cr /[(s-)gD]

Values for cr are typicallyrecorded on a Shield’s Diagram

cr >≈ b

(Boundary Reynolds Number)

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Settling velocities calculated assuming1) density of quartz2) Water temp = 20C3) Grain Shape: Spheroid4) Grain Roundness = subrounded

Particle settles at constant speed when the gravitational force is exactly balanced by

the sum of resistance forces.

This constant speed = settling velocity or fall velocity of the particle.

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Once the critical shear stress is exceeded the grains begin to move by: 1. rolling, 2. sliding, or 3. saltation.

a. Saltation = bedloadb. Modified saltationc. Full suspension

b increasing

Analysis of experimental data yields the following useful criteria:1.Pure Bedload: τb > τcr & ws/u* > 32.Suspension: ws/u* ≤ 1

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Properties of Saltation in Water

1.Hop Height < 10 particle diameters2.Hop Length < 100 particle diameters3.Grain Velocity < Fluid flow velocity

Saltating Particle (series of short hops)

Photograph of wind-borne motion of sand and silt in saltation and suspension

Chepil (1945)

Saltation

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Suspended-sediment transport

Properties of Suspension Trajectory

1.Trajectory Height < flow depth2.Trajectory Length >> particle diameter3.Grain Velocity ≈ Fluid flow velocity

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Smith, J.D., 1999, Flow and suspended-sediment transport in the Colorado River near National Canyon, in Webb, R.H., Schmidt, J.C., Marzolf, G.R., and Valdez, R.A., eds., The Controlled Flood in Grand Canyon, Volume 110: American Geophysical Union Geophysical Monograph, p. 71-98.

Suspended Sediment Concentration Profiles

Notice volume of fluid >> volume of suspended sand

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z

y

z

ssss uq Sediment discharge per unit width:Values for the following mean quantities are required in order to calculate rates of sediment transport:

1) s = average thickness of sediment transport layer2) <us> = average velocity of moving sediment3) <s> = average volume concentration of moving sediment

Calculating of rates of sediment transport.

Sediment discharge per unit widthor Volume flux of sediment= {(V × <s>) × <us>} / Aand has unit of Length2/Time